For one thing I don't really agree with the criticism that Picard was out of character in First Contact. Sure, he's in "action movie" mode, which made him a bit angrier than usual. He certainly acted in a different manner in "I, borg" but it's also possible that it was still eating away at him. It could have been boiling up inside him and the events of First Contact are what cause him to snap. In fact it's the scenes with Picard in First Contact that are the most interesting.
That said, I think Into Darkness is the better movie. I feel like it had a deeper message, I mean what is FC trying to say? There's so much going on at once.
They're both good movies though. I love first contact's score.